Download ENERGY - Katy Independent School District

What is Work?
• Work is when someone/thing creates a
change on an object
– Change in position (when fighting a force)
– Change in speed
– Change in Temperature
Doing Work
• Inertia: an object at rest tends to stay at rest, while
an object in motion tends to stay in motion with a
constant velocity, UNLESS ACTED ON BY A
NET OUTSIDE FORCE.
• The Conservation of Momentum: the total
momentum (value of motion) of a system is a
constant, UNLESS ACTED ON BY A NET
OUTSIDE FORCE.
• Since work is the act of creating a change, the
only thing capable of doing work is a force.
• FORCE CAUSES CHANGE
– SO FORCES ARE THE ONLY THING THAT CAN
DO WORK. (If any object is force free, then no work
can be done on it.)
Calculating Work
• Work = Force (parallel to displacement)*displacement
W = F//d
Force
q
Displacement
(d)
F//
Units of work
• Since Work = Force * displacement
• Force = Newton = kgm/s2
• Displacement = meters (m)
• The unit for work is …
• 1) Nm (Newton-meter)
• 2) Kg m2/s2
• 3) Joule (J)
• 1 Nm = 1 kg m2/s2 = 1 J
Do all forces do work?
• All forces CAN do work, but DON’T.
• For a force to do any amount of work, the force
must create a change on the object (move it).
• A person pushing a wall that does not move, does
no work on the wall.
• A person holding a 200 pound weight over their
head, does no work (he did to lift it, but not to
hold it.)
• This doesn’t make sense. Holding 200 pounds
over one’s head makes one tired (and sore), so
work must be done…
Kinds of Work
The number one confusion point for people is the
fact that the term work is an “umbrella word”
covering many different types of work.
Work
Mechanical
Biological
The truth is we are
often very bad at
identifying the type
of work we are
talking about. This is
Electrical
where most of the
Others confusion comes from.
Let’s look at these again:
• Does a person holding a 200 pound weight
over their head do work?
• Mechanical work: No the person is not
changing anything about the 200 pounds.
• Biological Work: Yes, the person’s body is
going through several types of changes
(thermal, chemical, and physical) to hold
the weight up.
What does it take to do work?
• In order to be able to generate a force to
create a change (do work) you must have a
source of energy that you can tap into.
• Energy allows you to be able to do work.
Force// Vs Distance graphs
• A visual tool we can often use is a
force// vs. distance graph.
• The area between the graph’s curve and
distance axis is the work that is done.
F//
F//
Work
Distance
Work
Distance
The work done by a spring
• A spring can do work two ways:
One is launching an object
Fspring i
F//
Dx
0N
Launched
work
0m
Dx
Distance
The work done by a spring
• The other way is to stop a moving object:
Vimpact
Distance
0m
0N
Dx
F//
Fspring f
Dx
work
Calculating the work of a spring
Fspring i
In either case the graphs make a triangle
Area = (1/2)(Base)(Height)
F//
work
0N
We also know that Fspring = -kDx
0m
Work = Area = (1/2)(Base)(Height)
Dx
Distance
0m
Work = (1/2)(Dx)(kDx)
0N
Work = (1/2)k(Dx)2
F//
Fspring f
Dx
work
What is Energy?
• The ability to do work
– The ability to create a change
• Energy comes in many forms
– Mechanical
• Potential
• Kinetic
–
–
–
–
Electrical
Thermal
Nuclear
Chemical
• It can be transformed from one form to another
• Like work, it is measured in Joules
Mechanical Energy
• Deals with the energy an object has because of
either it’s motion (kinetic energy), and/or the
outside forces acting on the object trying to make
it move (potential energy)
• A car moving at 50 mph can do a lot of damage to
a pedestrian if they hit--this is because of the
car’s motion.
• On the other hand, a 16 pound bowling ball being
held 10 ft above a person’s head (but not moving)
can be dangerous, because the force due to gravity
pulls down on the ball. The ball has the potential
to fall on the person’s head. The ball is not
falling, BUT IT COULD because of the force of
gravity.
Potential Energy
• Energy that is not being applied to the object’s
motion, BUT IT COULD BE LATER ON.
• It is the work done by something, other than you
(such as gravity), naturally on its own.
– Gravity causing things to fall
– Attraction/repulsion of electrical charges
– Expansion/contraction of a spring
• Potential energy depends on the position and
condition of the object (the forces that act on it).
• Think of a stretched rubber band on a slingshot. It has potential
energy due to its position. If the rubber band is released, it is capable
of doing work.
• Some call potential energy “stored energy” but
that term is very misleading (the energy does not
come from the object).
Gravitational Potential Energy
• Potential Energy due to gravity (Epg).
– Gravity is always trying to do work on objects by
pulling them down to the ground.
• Epg of an object is equal to the work done by
gravity to make an object fall.
• Work = Force*distance
• Workgravity = Forcegravity* distance dropped = mag(-h)
• Since ag = -9.8 m/s/s we use g. (g = 9.8 m/s/s)
• Epg = mgh
• Gravitational potential energy = /Fg/ * height
Calculating Epg
• Calculate the change in potential energy of
8 million kilograms of water dropping 50 m
over Niagara Falls.
• Know: m= 8 million kg
h = 50 m
g = 9.8 m/s2
• EPg = mgh
=(8,000,000 kg)(9.8 m/s2)(50 m)
= 3,920,000,000 J or 3.92 x109 J
Elastic Potential Energy
• Since a compressed spring wants to expand, and is
willing to do work on any object in the way of its
expansion, we call the work done by a spring the
elastic potential energy (Epel).
• This is also true for a stretched spring. It wants to
contract back to its original length, and will pull
anything attached to it.
• Some people call the elastic potential energy of a
spring the potential energy of a spring (Eps).
• elastic potential energy (Epel) is a more general name.
• (Eps) = work of a spring = (1/2)k(Dx)2
Kinetic Energy
• Energy of motion
– It is the energy an object has BECAUSE it is
moving. It IS NOT, IN ANY WAY, BY NO
MEANS the energy an object uses to keep moving.
(REMEMBER INERTIA).
• Depends on the mass and velocity of the object.
• Kinetic energy = (½)(mass)(velocity)2
Ek = (½)mv2
• Notice an object’s velocity has a greater impact
on its kinetic energy than it’s mass.
Work - Energy Theorem
• The work done on an object is defined as
the change in that object’s energy.
• Work = Change in Ep + Change in Ek
• W = DEp+ DEk
Work - Energy Theorem
• A moving object is capable of doing work.
– It can lose some of it’s kinetic energy (slow down) and
create a change on another object in the process.
–
–
–
–
Car hitting an object
A bat hitting a ball
Electrical charges moving through a wire
Hot steam moving the turbines of an electrical generator
• An object can also convert it’s potential energy
into kinetic energy so that it can do work.
Work
Kinetic Energy
Potential Energy
Net Work
• This is the overall work done on an object
• The net work is done by the net force acting on an
object
• The net work always equals the change in kinetic
energy
• Fnet//d = (1/2) mvf2 - (1/2) mvi2
• Objects in equilibrium never have any net work
done on them
• Fnet = 0 N
• Objects that move with a constant speed, never
have any net work done on them.
A quick comparison
Objects A and B are initially sliding on smooth ice and come to a
rough surface. Object A slides a distance of D as it comes to a stop.
How far (in terms of D) will object B have to slide to also come to a
stop? (The coefficient of kinetic friction is the same for both boxes.)
VA
Rest
mA
mA
D
Since object B has twice the
velocity of A it has 4X the
VB = 2VA
EK. This means friction must
mB
do 4X the work on B than on A.
And since the masses of A and B are the same, they both have the same
frictional force. So object B must slide 4X farther than object A to do all
that work. This is why you should never speed when driving.
Another comparison
Objects A and B are initially sliding on smooth ice and come a
rough surface. Object A slides a distance of D as it comes to a stop.
How far (in terms of D) will object B have to slide to also come to a
stop? (The coefficient of kinetic friction is the same for both boxes.)
VA
Rest
mA
mA
D
Since object B has 2X the
mass of object A, it has 2X the
VB = VA
mB = 2mA
EK of A. This means friction must
do 2X the work on B than on A.
Because Object B has 2X the mass of object A it also has 2X the
frictional force of object A. So object B slides the same distance as
object A.
Conservative forces.
• Some forces (such as gravity and electrical forces)
convert the work needed to overcome them, into
potential energy. This means that the energy you
used to move an object can be given back later on.
• For example, you do 30 joules of work to lift a
block (you had to fight gravity to lift it). The
block now has 30 joules of gravitational potential
energy that can be used later on.
• Gravity is called a CONSERVATIVE FORCE.
These forces conserve the amount of mechanical
energy in a system.
• They convert EK into EP and vice versa.
Conservation means to save. The total energy in a
conservative system is a constant.
Non-conservative forces
• Other forces, such as friction, convert the work
done on an object into heat.
• Heat is a form of energy, but not one we can ever
use again. Thus some say that the energy is “lost”.
• You push a block across a rough floor. Once it
stops moving, it does not return on its own to the
starting point.
• Non-conservative forces often create heat--they do
not keep the amount of mechanical energy of a
system constant.
• Work = Change in Ep + Change in Ek + Heat(if any)
• W = DEp+ DEk + Q (if any)
Law of Conservation of Energy
• It states: Energy cannot be created nor
destroyed. It is transformed from one form
into another, but the total amount of energy
never changes.
• Example - when gasoline combines with oxygen in a car’s
engine, the chemical Ep of the fuel is converted to
molecular Ek, and thermal energy. Some of this energy is
transferred to the piston and some of this energy causes the
motion of the car. The rest of the energy escapes (“is
lost”) the system of the engine (as heat) and enters the
environment.
• “Lost energy” is not energy that is destroyed, it is simply
energy we cannot use.
Application of the Conservation
of Energy
• If there are only conservative forces acting
on a system then we can say:
– The starting total mechanical energy = the final mechanical energy
• ETi = ETf
• Epi + Eki = Epf + Ekf
• The conservation of energy simplifies many
complex problems into one easy process.
Sample problem 1
• A block is released from rest at the top of a
smooth incline and slides to the bottom.
What is the block’s final speed when it
reaches the bottom?
5m
Vf
5m
0m
Epgi = mass(9.8m/s/s)(5m)
Epgf = mass(9.8m/s/s)(0m)
Eki = (1/2)mass(0 m/s)2
Ekf = (1/2)mass(Vf)2
ETi = mass(9.8m/s/s)(5m)
ETf = (1/2)mass(Vf)2
mass(9.8m/s/s)(5m) = (1/2)mass(Vf)2
2(9.8m/s/s)(5m) = V
Start
Ep
Middle
EK
The total energy at
one point is the
same for all points
for a conservative
system
Ep
EK
End
Ep
EK
Sample problem 2
• A ball held from a height of 5 meters is
dropped. What is the speed of the ball
when it hits the ground?
5m
5m
Vf
0m
Epgi = mass(9.8m/s/s)(5m)
Epgf = mass(9.8m/s/s)(0m)
Eki = (1/2)mass(0 m/s)2
Ekf = (1/2)mass(Vf)2
ETi = mass(9.8m/s/s)(5m)
ETf = (1/2)mass(Vf)2
mass(9.8m/s/s)(5m) = (1/2)mass(Vf)2
2(9.8m/s/s)(5m) = V
Independence of Path
• When a system is conservative, the path the
object takes to go from point A to point B
has no impact (is independent of) …
• The work needed to go there
• The change in Ep
• The change in Ek